"When they refused to move, minimum force had to be used. So rubber bullets were fired," Captain Nondumiso Mpantsha, a police spokeswoman, said.
About 150 health workers had tried to enter the 3,000-bed hospital.
"Some people were hit in their legs, some in their bodies. Some of the people were hurt [by the rubber bullets]," Hamilton Maswanganyi, a hospital gardener, said.
"Some people were hit in their legs, some in their bodies [by the rubber bullets]"
He said strikers were upset that their colleagues were still working inside.
"We wanted to talk to them but the police doesn't allow us," he said.
Police also fired rubber bullets at striking teachers who tried to cross a barricade near a Johannesburg highway.
Public sector unions have demanded an 8.6 per cent wage increase - more than twice the rate of inflation - and a monthly housing allowance of $137.
One hospital clerical worker said she was taking part in the strike because her salary is not sufficient enough for her to live in a house.
"It's difficult. I'm living in a shack. I can't afford to buy a house," she said, asking not to be named.
However, the government on Thursday signed its last offer of just a seven per cent increase plus $96 for housing, which will cost the state $687m.
The public services ministry says the deal will be implemented unilaterally if unions fail to sign on within 21 days.
About 1.3 million South African state workers began an open-ended strike on Wednesday after rejecting the government deal.
|Army personnel helped out at a hospital in Durban after nurses joined the strike [AFP]
Al Jazeera's Haru Mutasa, reporting from Soweto, said the unions and their supporters do not believe the government when it says that it has no money.
"They say they see politicians living lavish lifestyles, they question why there was money for the football World Cup [staged in South Africa] and say they are tired of corruption allegations in government departments and that they will not put up with it anymore," she said.
Health workers, like police and immigration agents, are considered essential services and not allowed to strike, but Durban officials reported that nurses had joined the nationwide action.
Doctors were feeding patients, wheeling them to their beds and even cleaning the hospital, Nonto Beko, a spokesman for the 922-bed King Edward VIII Hospital, told the AFP news agency.
"We basically do not have anyone in the hospital except the doctors and the nurses from the army. People are all out striking," Beko said.
"We are in the process of getting private cleaners to clean the hospital because the doctors have been basically doing everything."
So far protests have been limited to small groups picketing outside schools and hospitals, but the government criticised the unrest that had broken out in some areas.
"Cabinet condemns unreservedly the violence, intimidation and the acts bordering on thuggery and criminality, that has characterised the strike in parts of the country," Themba Maseko, a cabinet spokesman, told reporters.
"The defence force will be on stand-by to provide assistance in emergency and life-threatening situations such as providing urgently needed medical care."
Rowdy strikes are annual events in South Africa, where contracts come up for renewal midyear.
This year, public workers postponed their strike threat until after the football World Cup, a gesture that did little to close the gap with government over wages.
Jacob Zuma, the South African president, is under pressure to provide expanded access to housing, water and electricity for the poorest South Africans.
The country's unions are politically powerful and a key ally of Zuma's ruling African National Congress, but tensions have erupted over both wages and general economic policy.
The last big public sector strike in South Africa took place in 2007 when a four-week strike by 600,000 state workers cost the economy several million lost working-days, discouraged investors and angered the public.